\documentclass[11pt]{article}
\usepackage{graphicx,bm,amssymb,amsmath,amsthm}
\input{macros}

\begin{document}
\title{\mpspack\ tutorial}
\author{Alex Barnett\footnote{Department of Mathematics, Dartmouth College,
Hanover, NH, 03755, USA}
\ and
Timo Betcke\footnote{Department of Mathematics,
University College London, Gower Street, London, WC1E 6BT, UK}}

\date{\today}   % how pipe from getrevisionnumber + 1?

\maketitle
\begin{abstract}
This tutorial shows how a variety of two-dimensional Laplace and Helmholtz
boundary-value and eigenvalue problems
may be numerically solved simply and accurately with the \mpspack\ toolbox
for \matlab. We assume basic familiarity with \matlab\
and with linear partial differential equations.
%concept of particular-solution type numerical methods is assumed.
\end{abstract}

\setcounter{tocdepth}{2}
\tableofcontents

\section{About this tutorial}

This tutorial is designed for `bottom-up' learning of the features
of \mpspack, i.e.\ by progressing through simple examples.
In that sense it complements the user manual which describes
the theoretical framework in broad strokes and therefore could
be considered `top-down'.
We will skip most of the mathematics behind the techniques,
focusing on computing and plotting useful PDE solutions.
We hope you will try each command as you read!

Throughout we will identify the plane $\mathbb{R}^2$ with the complex
plane $\mathbb{C}$, by the usual map $z=x+iy$. In other words
$(2,3)$ and $2+3i$ represent the same point.
We use {\tt teletype} font to designate commands that may be typed
at the \matlab\ prompt.
You may get help on any \mpspack\ command by typing {\tt help command}.
All the code examples in this document, including code to generate the
figures, is found in the {\tt examples/} directory.
The codes for Sections \ref{s:lap}--\ref{s:qpsc} are named
\verb@tut_*.m@ according to the section names in {\tt tutorial.tex}.

Computation times are reported for a single core (mostly what MATLAB
uses) of an Intel laptop CPU (either Core Duo from 2006, or i7-3720QM
from 2012).

\input{tut_lap}
\input{tut_conv}
\input{tut_ext}
\input{tut_poly}
\input{tut_scatt}
\input{tut_layer}
\input{tut_qpsc}
\input{tut_evp}
\input{tut_exa}

\bibliographystyle{siam} 
\bibliography{alexrefs}
\end{document}
